messages listlengths 2 2 | meta dict |
|---|---|
[
{
"role": "user",
"content": "Resolve this equation and give the result. 19 + 162x^2 - 85x = 101"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 19 + 162x^2 - 85x = 101 $\n\nMove all terms to the left (standard form):\n$ 162x^2 + -85x + -82 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5500
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence... | {
"type": "optimization",
"seed": 1337,
"index": 5501
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Prove that $f(x)=6x^2+5x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+5x+0$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'... | {
"type": "optimization",
"seed": 1337,
"index": 5502
} |
[
{
"role": "user",
"content": "Solve this equation step by step. -111 + 364x = -483"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -111 + 364x = -483 $\n\nMove all terms to the left (standard form):\n$ 364x + 372 = 0 $\n\nIsolate the $x$ term:\n$ 364x = -372 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5503
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Compute the determinant: $A=\\begin{pmatrix}4&-9\\\\-7&3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}4&-9\\\\\\-7&3\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5504
} |
[
{
"role": "user",
"content": "Solve this equation accurately. -520 - 614 = 675x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -520 - 614 = 675x $\n\nMove all terms to the left (standard form):\n$ -675x + -1134 = 0 $\n\nIsolate the $x$ term:\n$ -675x = 1134 $\n\nDivide both sides ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5505
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Differentiate with respect to $x$: $f(x) = \\ln(1x + -1)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(1x + -1) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{1}{1... | {
"type": "calculus",
"seed": 1337,
"index": 5506
} |
[
{
"role": "user",
"content": "Determine the correct solution for the given equation. Solve for $x$ (in radians): tan(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alp... | {
"type": "trigonometry",
"seed": 1337,
"index": 5507
} |
[
{
"role": "user",
"content": "Solve the equation and state the result. -32x^2 + 139 - 49x = -82"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -32x^2 + 139 - 49x = -82 $\n\nMove all terms to the left (standard form):\n$ -32x^2 + -49x + 221 = 0 $\n\nApply the quadratic formula:\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5508
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Solve for $x$ (in radians): cos(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = 1 $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\alpha = \\arccos(1) = 0 $\n\nThe gener... | {
"type": "trigonometry",
"seed": 1337,
"index": 5509
} |
[
{
"role": "user",
"content": "Solve the equation and provide the final value. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, h... | {
"type": "optimization",
"seed": 1337,
"index": 5510
} |
[
{
"role": "user",
"content": "solve: \n\n -6x - 17x^2 - 143 = 45"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -6x - 17x^2 - 143 = 45 $\n\nMove all terms to the left (standard form):\n$ -17x^2 + -6x + -188 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5511
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Find the modular inverse of 5 modulo 14, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $5\\cdot a^{-1} \\equiv 1 \\pmod{14}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantees integers $x,y$ with:\n$ 5... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5512
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Compute the determinant: $A=\\begin{pmatrix}-2&-6\\\\-3&-3\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-2&-6\\\\\\-3&-3\\end{pmatrix} $\n\n... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5513
} |
[
{
"role": "user",
"content": "Find the answer to the following equation. Differentiate with respect to $x$: $f(x) = \\ln(7x + 6)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(7x + 6) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{7}... | {
"type": "calculus",
"seed": 1337,
"index": 5514
} |
[
{
"role": "user",
"content": "solve: \n\n Differentiate with respect to $x$: $f(x) = 4e^{-2x}$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4e^{-2x} $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-8e^{-2x}} $"
}
] | {
"type": "calculus",
"seed": 1337,
"index": 5515
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. -36x + 22x^2 - = 2"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -36x + 22x^2 - = 2 $\n\nMove all terms to the left (standard form):\n$ 22x^2 + -36x + -2 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5516
} |
[
{
"role": "user",
"content": "Solve the equation and calculate the result. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\... | {
"type": "optimization",
"seed": 1337,
"index": 5517
} |
[
{
"role": "user",
"content": "Solve this equation accurately. Evaluate: ((191 + -828/18) * 9) + 5^2 - log_2(4) + (-411 mod 20) + floor(-8/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((191 + -828/18) * 9) + 5^2 - log_2(4) + (-411 mod 20) + floor(-8/2) $\n\nCompute each c... | {
"type": "arithmetic",
"seed": 1337,
"index": 5518
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Evaluate: ((-131 + 680/20) * 7) + 9^2 - log_10(100000) + (20 mod 7) + floor(161/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-131 + 680/20) * 7) + 9^2 - log_10(100000) + (20 mod 7) + floo... | {
"type": "arithmetic",
"seed": 1337,
"index": 5519
} |
[
{
"role": "user",
"content": "Work through and solve this equation. Differentiate with respect to $x$: $f(x) = (-5x + 8)\\sin(6x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (-5x + 8)\\sin(6x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{-5... | {
"type": "calculus",
"seed": 1337,
"index": 5520
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. 144 + 619x = -239"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 144 + 619x = -239 $\n\nMove all terms to the left (standard form):\n$ 619x + 383 = 0 $\n\nIsolate the $x$ term:\n$ 619x = -383 $\n\nDivide b... | {
"type": "linear_equation",
"seed": 1337,
"index": 5521
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Compute the indefinite integral: $\\int \\ln(4x + 5)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(4x + 5)\\,dx $\n\nUse standard antiderivatives (and integration by parts i... | {
"type": "calculus",
"seed": 1337,
"index": 5522
} |
[
{
"role": "user",
"content": "Compute the solution of this mathematical equation. Differentiate with respect to $x$: $f(x) = 6x^3 + 7x^2 + 5x + 6$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 6x^3 + 7x^2 + 5x + 6 $\n\nApply the standard differentiation rules:\n$ ... | {
"type": "calculus",
"seed": 1337,
"index": 5523
} |
[
{
"role": "user",
"content": "Please determine the value of this equation. Compute the indefinite integral: $\\int \\ln(4x + -1)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int \\ln(4x + -1)\\,dx $\n\nUse standard antiderivatives (and integration by parts ... | {
"type": "calculus",
"seed": 1337,
"index": 5524
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. Evaluate: ((73 + -210/21) * 11) + 5^4 - log_10(100000) + (144 mod 12) + floor(-89/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((73 + -210/21) * 11) + 5^4 - log_10(100000) + (144 mod 12) + fl... | {
"type": "arithmetic",
"seed": 1337,
"index": 5525
} |
[
{
"role": "user",
"content": "Evaluate and solve the given equation. Evaluate: ((-45 + -78/6) * 14) + 7^3 - log_2(2) + (-387 mod 7) + ceil(-157/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-45 + -78/6) * 14) + 7^3 - log_2(2) + (-387 mod 7) + ceil(-157/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 5526
} |
[
{
"role": "user",
"content": "Can you evaluate this math equation? Differentiate with respect to $x$: $f(x) = 3\\sin(5x) + 7\\cos(3x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 3\\sin(5x) + 7\\cos(3x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \... | {
"type": "calculus",
"seed": 1337,
"index": 5527
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. Differentiate with respect to $x$: $f(x) = \\ln(5x + -1)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(5x + -1) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{5}{5x + ... | {
"type": "calculus",
"seed": 1337,
"index": 5528
} |
[
{
"role": "user",
"content": "Calculate and solve this equation. 8x^2 - 142x + 72 = 178"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 8x^2 - 142x + 72 = 178 $\n\nMove all terms to the left (standard form):\n$ 8x^2 + -142x + -106 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5529
} |
[
{
"role": "user",
"content": "Find the correct solution for this equation. Differentiate with respect to $x$: $f(x) = \\ln(3x + 0)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = \\ln(3x + 0) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\boxed{\\frac{... | {
"type": "calculus",
"seed": 1337,
"index": 5530
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Evaluate: ((108 + 888/24) * 14) + 11^4 - log_2(16) + (-375 mod 10) + floor(-45/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((108 + 888/24) * 14) + 11^4 - log_2(16) + (-375 mod 10) + floor(-45/... | {
"type": "arithmetic",
"seed": 1337,
"index": 5531
} |
[
{
"role": "user",
"content": "Please compute and solve this equation. 843x + 500 = -810"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 843x + 500 = -810 $\n\nMove all terms to the left (standard form):\n$ 843x + 1310 = 0 $\n\nIsolate the $x$ term:\n$ 843x = -1310 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5532
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\partial^2... | {
"type": "optimization",
"seed": 1337,
"index": 5533
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. 259x + 12 = 26"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 259x + 12 = 26 $\n\nMove all terms to the left (standard form):\n$ 259x + -14 = 0 $\n\nIsolate the $x$ term:\n$ 259x = 14 $\n\nDivide both sides by ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5534
} |
[
{
"role": "user",
"content": "Solve the math equation and present the result. 899 + 697 = -190x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 899 + 697 = -190x $\n\nMove all terms to the left (standard form):\n$ 190x + 1596 = 0 $\n\nIsolate the $x$ term:\n$ 190x = -1596 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 5535
} |
[
{
"role": "user",
"content": "Please solve the equation presented here. Prove that $f(x,y)=\\frac12(6x^2+8y^2)+5x+3y+-10$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(6x^2+8y^2)+5x+3y+-10 $\n\n$ \\frac{\\partial^2 f}{\\... | {
"type": "optimization",
"seed": 1337,
"index": 5536
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Evaluate: ((74 + -63/9) * 3) + 12^4 - log_5(15625) + (-193 mod 27) + round(-111/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((74 + -63/9) * 3) + 12^4 - log_5(15625) + (-193 mod 27) + round(-111/2) $\n... | {
"type": "arithmetic",
"seed": 1337,
"index": 5537
} |
[
{
"role": "user",
"content": "Work out the result of this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}5&4&-2\\\\\\-3&0&0\\\\\\-1&-2&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-21\\\\\\9\\\\\\12\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$ (e.g.... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5538
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\... | {
"type": "optimization",
"seed": 1337,
"index": 5539
} |
[
{
"role": "user",
"content": "Please find the value of this math equation. Find the modular inverse of 4 modulo 7, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $4\\cdot a^{-1} \\equiv 1 \\pmod{7}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guarantee... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5540
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. Evaluate: ((-128 + -646/19) * 3) + 12^2 - log_2(32) + (-89 mod 23) + ceil(-26/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-128 + -646/19) * 3) + 12^2 - log_2(32) + (-89 mod 23) + ceil(-26/2) $\n\nCo... | {
"type": "arithmetic",
"seed": 1337,
"index": 5541
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 5542
} |
[
{
"role": "user",
"content": "Please find the solution of this equation. 13x^2 + 124 + 149x = -111"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 13x^2 + 124 + 149x = -111 $\n\nMove all terms to the left (standard form):\n$ 13x^2 + 149x + 235 = 0 $\n\nApply the quadratic formul... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5543
} |
[
{
"role": "user",
"content": "Compute the result for the following equation. Differentiate with respect to $x$: $f(x) = (6x + 7)\\sin(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = (6x + 7)\\sin(1x) $\n\nApply the standard differentiation rules:\n$ f'(x) = \\b... | {
"type": "calculus",
"seed": 1337,
"index": 5544
} |
[
{
"role": "user",
"content": "Find the correct answer to the equation below. 847 - 894x = 919"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 847 - 894x = 919 $\n\nMove all terms to the left (standard form):\n$ -894x + -72 = 0 $\n\nIsolate the $x$ term:\n$ -894x = 72 $\n\nDivide bo... | {
"type": "linear_equation",
"seed": 1337,
"index": 5545
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Compute $(109+-96) \\bmod 3$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (109+-96) \\bmod 3 $\n\nUse the rule that addition is compatible with reduction ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5546
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$... | {
"type": "optimization",
"seed": 1337,
"index": 5547
} |
[
{
"role": "user",
"content": "Determine the solution for this math problem. Solve for $x$ (in radians): tan(x) = 1."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = 1 $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(1) = 0.785398 $\n\n... | {
"type": "trigonometry",
"seed": 1337,
"index": 5548
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Compute the indefinite integral: $\\int (-5x + -4)\\sin(1x)\\,dx$."
},
{
"role": "assistant",
"content": "Compute the indefinite integral:\n$ \\int (-5x + -4)\\sin(1x)\\,dx $\n\nUse standard antiderivatives (and integratio... | {
"type": "calculus",
"seed": 1337,
"index": 5549
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. -40 + 199x + 39x^2 = 130"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -40 + 199x + 39x^2 = 130 $\n\nMove all terms to the left (standard form):\n$ 39x^2 + 199x + -170 = 0 $\n\nApply the quadratic formu... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5550
} |
[
{
"role": "user",
"content": "Find the numerical solution to this equation. Solve the $3\\times 3$ linear system $Ax=b$.\n$A=\\begin{pmatrix}-3&-3&2\\\\\\1&5&-2\\\\\\-1&-3&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-3\\\\\\-3\\\\\\1\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5551
} |
[
{
"role": "user",
"content": "solve Prove that $f(x,y)=\\frac12(9x^2+7y^2)+4x+6y+-2$ is convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Compute the Hessian matrix $H$.\n\n$ f(x,y)=\\frac12(9x^2+7y^2)+4x+6y+-2 $\n\n$ \\frac{\\partial^2 f}{\\partial x^2} = 9,\\quad \\frac{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 5552
} |
[
{
"role": "user",
"content": "Please solve this math problem. Evaluate: ((192 + 414/23) * 8) + 10^3 - log_4(4096) + (-311 mod 21) + ceil(-117/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((192 + 414/23) * 8) + 10^3 - log_4(4096) + (-311 mod 21) + ceil(-117/2) $\n\nComput... | {
"type": "arithmetic",
"seed": 1337,
"index": 5553
} |
[
{
"role": "user",
"content": "Determine the result of this mathematical equation. Differentiate with respect to $x$: $f(x) = -5\\sin(9x) + 1\\cos(1x)$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = -5\\sin(9x) + 1\\cos(1x) $\n\nApply the standard differentiation ru... | {
"type": "calculus",
"seed": 1337,
"index": 5554
} |
[
{
"role": "user",
"content": "solve: \n\n 30x^2 - 185 + 197 = 34x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 30x^2 - 185 + 197 = 34x $\n\nMove all terms to the left (standard form):\n$ 30x^2 + -34x + 12 = 0 $\n\nApply the quadratic formula:\n$ x = \\frac{-b \\pm \\sqrt{b^2 ... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5555
} |
[
{
"role": "user",
"content": "Can you compute this equation? Solve for $x$ (in radians): tan(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(-\\frac{1}... | {
"type": "trigonometry",
"seed": 1337,
"index": 5556
} |
[
{
"role": "user",
"content": "Determine the solution of the equation provided. Evaluate: ((92 + -105/21) * 1) + 5^4 - log_2(64) + (-208 mod 20) + floor(-172/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((92 + -105/21) * 1) + 5^4 - log_2(64) + (-208 mod 20) + floor(-172/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 5557
} |
[
{
"role": "user",
"content": "Provide the solution to the following equation. -778 - 354x = -807"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -778 - 354x = -807 $\n\nMove all terms to the left (standard form):\n$ -354x + 29 = 0 $\n\nIsolate the $x$ term:\n$ -354x = -29 $\n\nDivi... | {
"type": "linear_equation",
"seed": 1337,
"index": 5558
} |
[
{
"role": "user",
"content": "Please compute the answer to this equation. Compute the determinant: $A=\\begin{pmatrix}-4&-3\\\\-4&2\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-4&-3\\\\\\-4&2\\end{pmatrix} $\n\nU... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5559
} |
[
{
"role": "user",
"content": "SOLVE THIS NOW: Evaluate: ((103 + -294/21) * 8) + 10^5 - log_4(4096) + (158 mod 14) + floor(88/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((103 + -294/21) * 8) + 10^5 - log_4(4096) + (158 mod 14) + floor(88/2) $\n\nCompute each component:\... | {
"type": "arithmetic",
"seed": 1337,
"index": 5560
} |
[
{
"role": "user",
"content": "Please solve this math problem. 647 + 225 = -738x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 647 + 225 = -738x $\n\nMove all terms to the left (standard form):\n$ 738x + 872 = 0 $\n\nIsolate the $x$ term:\n$ 738x = -872 $\n\nDivide both sides by t... | {
"type": "linear_equation",
"seed": 1337,
"index": 5561
} |
[
{
"role": "user",
"content": "Compute the outcome of this equation. Evaluate: ((89 + -902/22) * 7) + 7^2 - log_6(216) + (-202 mod 10) + floor(-65/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((89 + -902/22) * 7) + 7^2 - log_6(216) + (-202 mod 10) + floor(-65/2) $\n\nComp... | {
"type": "arithmetic",
"seed": 1337,
"index": 5562
} |
[
{
"role": "user",
"content": "Solve the following mathematical problem. -137 + 801x = 617"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -137 + 801x = 617 $\n\nMove all terms to the left (standard form):\n$ 801x + -754 = 0 $\n\nIsolate the $x$ term:\n$ 801x = 754 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5563
} |
[
{
"role": "user",
"content": "Find the value that satisfies this equation. Prove that $f(x)=6x^2+2x+-1$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=6x^2+2x+-1$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f'(x... | {
"type": "optimization",
"seed": 1337,
"index": 5564
} |
[
{
"role": "user",
"content": "Please solve this mathematical equation. Solve for $x$ (in radians): tan(x) = \\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{1}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$ \\alpha = \\arctan(\\... | {
"type": "trigonometry",
"seed": 1337,
"index": 5565
} |
[
{
"role": "user",
"content": "Can you determine the solution of this equation? Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, ... | {
"type": "optimization",
"seed": 1337,
"index": 5566
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Evaluate: ((-92 + 768/24) * 19) + 2^2 - log_5(625) + (184 mod 28) + floor(174/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-92 + 768/24) * 19) + 2^2 - log_5(625) + (184 mod 28) + floor(174/2) $\... | {
"type": "arithmetic",
"seed": 1337,
"index": 5567
} |
[
{
"role": "user",
"content": "Resolve the equation provided. Solve for $x$ (in radians): sin(x) = -\\frac{1}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{1}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ \\alpha = \\arcsin(-\\frac{1}... | {
"type": "trigonometry",
"seed": 1337,
"index": 5568
} |
[
{
"role": "user",
"content": "Find the solution to this math problem. Solve for $x$ (in radians): cos(x) = -\\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ cos(x) = -\\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arccos(k)$ (principal value).\n$ \\al... | {
"type": "trigonometry",
"seed": 1337,
"index": 5569
} |
[
{
"role": "user",
"content": "Find the solution to this equation and report it. -40x^2 + 144 + 83 = -147x"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ -40x^2 + 144 + 83 = -147x $\n\nMove all terms to the left (standard form):\n$ -40x^2 + 147x + 227 = 0 $\n\nApply the quadrati... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5570
} |
[
{
"role": "user",
"content": "Determine the solution of the given equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 5571
} |
[
{
"role": "user",
"content": "Compute the correct solution for this equation. Compute $(-189+136) \\bmod 4$ and justify using modular arithmetic rules."
},
{
"role": "assistant",
"content": "Compute the modular sum:\n$ (-189+136) \\bmod 4 $\n\nUse the rule that addition is compatible with reduct... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5572
} |
[
{
"role": "user",
"content": "solve the follow equation, show ALL of your work: \n\n Prove that $(\\mathbb{Z}_29, +)$ is a group under addition modulo 29."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_29=\\{0,1,\\dots,28\\}$ with operation $+$ modulo $29$.\n\n**Closure:** If $a,b\... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5573
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Solve for $x$ (in radians): sin(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ sin(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arcsin(k)$ (principal value).\n$ ... | {
"type": "trigonometry",
"seed": 1337,
"index": 5574
} |
[
{
"role": "user",
"content": "Solve this mathematical equation for me. Evaluate: ((195 + 840/21) * 15) + 8^4 - log_2(2) + (-54 mod 6) + floor(63/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((195 + 840/21) * 15) + 8^4 - log_2(2) + (-54 mod 6) + floor(63/2) $\n\nCompute e... | {
"type": "arithmetic",
"seed": 1337,
"index": 5575
} |
[
{
"role": "user",
"content": "Please find and report the solution to this equation. Evaluate: ((-189 + 644/23) * 11) + 11^3 - log_8(8) + (227 mod 7) + floor(155/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((-189 + 644/23) * 11) + 11^3 - log_8(8) + (227 mod 7) + floor(15... | {
"type": "arithmetic",
"seed": 1337,
"index": 5576
} |
[
{
"role": "user",
"content": "Please determine the solution to this equation. Find the modular inverse of 10 modulo 27, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $10\\cdot a^{-1} \\equiv 1 \\pmod{27}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity gu... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5577
} |
[
{
"role": "user",
"content": "Compute and determine the solution to this equation. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=... | {
"type": "optimization",
"seed": 1337,
"index": 5578
} |
[
{
"role": "user",
"content": "Find the solution of the math equation below. Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hen... | {
"type": "optimization",
"seed": 1337,
"index": 5579
} |
[
{
"role": "user",
"content": "Can you find the solution to this equation? Evaluate: ((146 + -1012/22) * 9) + 6^5 - log_10(100) + (164 mod 4) + round(113/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((146 + -1012/22) * 9) + 6^5 - log_10(100) + (164 mod 4) + round(113/2) $... | {
"type": "arithmetic",
"seed": 1337,
"index": 5580
} |
[
{
"role": "user",
"content": "Find the result of the given mathematical equation. Solve for $x$ (in radians): tan(x) = \\frac{\\sqrt{2}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = \\frac{\\sqrt{2}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value... | {
"type": "trigonometry",
"seed": 1337,
"index": 5581
} |
[
{
"role": "user",
"content": "Resolve this equation and give the result. 398 - 189 = -441x"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 398 - 189 = -441x $\n\nMove all terms to the left (standard form):\n$ 441x + 209 = 0 $\n\nIsolate the $x$ term:\n$ 441x = -209 $\n\nDivide both... | {
"type": "linear_equation",
"seed": 1337,
"index": 5582
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Prove that $(\\mathbb{Z}_2, +)$ is a group under addition modulo 2."
},
{
"role": "assistant",
"content": "Consider $\\mathbb{Z}_2=\\{0,1,\\dots,1\\}$ with operation $+$ modulo $2$.\n\n**Closure:** If $a,b\\in\\mathbb{Z}_n$, ... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5583
} |
[
{
"role": "user",
"content": "Please resolve the math equation below. -521 + 111x = -740"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -521 + 111x = -740 $\n\nMove all terms to the left (standard form):\n$ 111x + 219 = 0 $\n\nIsolate the $x$ term:\n$ 111x = -219 $\n\nDivide both ... | {
"type": "linear_equation",
"seed": 1337,
"index": 5584
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Evaluate: ((120 + 14/14) * 7) + 11^3 - log_9(531441) + (-74 mod 24) + floor(-43/2)"
},
{
"role": "assistant",
"content": "Evaluate the expression:\n$ ((120 + 14/14) * 7) + 11^3 - log_9(531441) + (-74 mod 24) + floor(-43/2... | {
"type": "arithmetic",
"seed": 1337,
"index": 5585
} |
[
{
"role": "user",
"content": "Please work through this equation and solve it. Find the modular inverse of 9 modulo 14, and justify your answer."
},
{
"role": "assistant",
"content": "We want $a^{-1}$ such that $9\\cdot a^{-1} \\equiv 1 \\pmod{14}$.\n\nSince $\\gcd(a,m)=1$, Bézout's identity guar... | {
"type": "abstract_algebra",
"seed": 1337,
"index": 5586
} |
[
{
"role": "user",
"content": "Please compute the solution to this problem. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\... | {
"type": "optimization",
"seed": 1337,
"index": 5587
} |
[
{
"role": "user",
"content": "Evaluate the equation and solve it. -183 - 209x = 140"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ -183 - 209x = 140 $\n\nMove all terms to the left (standard form):\n$ -209x + -323 = 0 $\n\nIsolate the $x$ term:\n$ -209x = 323 $\n\nDivide both side... | {
"type": "linear_equation",
"seed": 1337,
"index": 5588
} |
[
{
"role": "user",
"content": "solve: \n\n 20x - 956 = -703"
},
{
"role": "assistant",
"content": "Solve the equation:\n$ 20x - 956 = -703 $\n\nMove all terms to the left (standard form):\n$ 20x + -253 = 0 $\n\nIsolate the $x$ term:\n$ 20x = 253 $\n\nDivide both sides by the coefficient of $x$:\n... | {
"type": "linear_equation",
"seed": 1337,
"index": 5589
} |
[
{
"role": "user",
"content": "Please evaluate and solve this equation. Solve the linear system $Ax=b$:\n$A=\\begin{pmatrix}6&-3\\\\\\3&3\\end{pmatrix},\\quad b=\\begin{pmatrix}-30\\\\\\-51\\end{pmatrix}.$"
},
{
"role": "assistant",
"content": "Solve $Ax=b$.\n$ A=\\begin{pmatrix}6&-3\\\\\\3&3\\en... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5590
} |
[
{
"role": "user",
"content": "Please solve this math problem. 38x^2 - 166 - 167x = 62"
},
{
"role": "assistant",
"content": "To solve the equation:\n$ 38x^2 - 166 - 167x = 62 $\n\nMove all terms to the left (standard form):\n$ 38x^2 + -167x + -228 = 0 $\n\nApply the quadratic formula:\n$ x = \\f... | {
"type": "quadratic_equation",
"seed": 1337,
"index": 5591
} |
[
{
"role": "user",
"content": "Solve this equation and return the solution. Solve for $x$ (in radians): tan(x) = -\\frac{\\sqrt{3}}{2}."
},
{
"role": "assistant",
"content": "Solve the trigonometric equation:\n$ tan(x) = -\\frac{\\sqrt{3}}{2} $\n\nLet $\\alpha = \\arctan(k)$ (principal value).\n$... | {
"type": "trigonometry",
"seed": 1337,
"index": 5592
} |
[
{
"role": "user",
"content": "Solve the mathematical equation provided below. Prove that $f(x)=9x^2+-6x+0$ is convex on $\\mathbb{R}$."
},
{
"role": "assistant",
"content": "Let $f(x)=9x^2+-6x+0$.\n\nA twice-differentiable function on $\\mathbb{R}$ is convex if $f''(x)\\ge 0$ for all $x$.\n\n$ f... | {
"type": "optimization",
"seed": 1337,
"index": 5593
} |
[
{
"role": "user",
"content": "Find the final answer to the given equation. Differentiate with respect to $x$: $f(x) = 4x^3 + -6x^2 + -12x + -13$."
},
{
"role": "assistant",
"content": "Differentiate the function:\n$ f(x) = 4x^3 + -6x^2 + -12x + -13 $\n\nApply the standard differentiation rules:\... | {
"type": "calculus",
"seed": 1337,
"index": 5594
} |
[
{
"role": "user",
"content": "Please evaluate the equation provided. Compute the determinant: $A=\\begin{pmatrix}3&0\\\\2&-4\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}3&0\\\\\\2&-4\\end{pmatrix} $\n\nUse $\\det... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5595
} |
[
{
"role": "user",
"content": "Find the solution to the equation shown. Show that $f(x,y)=x^2-y^2$ is not convex on $\\mathbb{R}^2$."
},
{
"role": "assistant",
"content": "Consider $f(x,y)=x^2-y^2$.\n\nCompute the Hessian:\n$ H=\\begin{pmatrix} \\frac{\\partial^2 f}{\\partial x^2} & \\frac{\\part... | {
"type": "optimization",
"seed": 1337,
"index": 5596
} |
[
{
"role": "user",
"content": "Determine the result of the equation below. Find $A^{-1}$ for $A=\\begin{pmatrix}-9&-4\\\\-2&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Find the inverse of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix} -9 & -4 \\\\ -2 & -6 \\end{pmatrix} $\n\nCompute... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5597
} |
[
{
"role": "user",
"content": "solve: \n\n Find all stationary points of $f(x)=x^4-2x^2$ and classify them."
},
{
"role": "assistant",
"content": "Compute the derivative:\n$ f(x)=x^4-2x^2 $\n$ f'(x)=4x^3-4x=4x(x^2-1). $\n\nStationary points satisfy $f'(x)=0$, hence:\n$ 4x(x^2-1)=0 \\Rightarrow x\... | {
"type": "optimization",
"seed": 1337,
"index": 5598
} |
[
{
"role": "user",
"content": "Please evaluate and compute this equation. Compute the determinant: $A=\\begin{pmatrix}-3&-7\\\\7&-6\\end{pmatrix}$."
},
{
"role": "assistant",
"content": "Compute the determinant of the $2\\times 2$ matrix:\n$ A=\\begin{pmatrix}-3&-7\\\\\\7&-6\\end{pmatrix} $\n\nUs... | {
"type": "linear_algebra",
"seed": 1337,
"index": 5599
} |
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